To rewrite \( 3 + 4 - \sqrt{45} \) as a complex number in the standard form \( a + bi \), we first simplify the expression.
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Calculate \( \sqrt{45} \): \[ \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5} \]
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Now substitute \( \sqrt{45} \) back into the expression: \[ 3 + 4 - \sqrt{45} = 3 + 4 - 3\sqrt{5} \]
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Combine the real numbers: \[ 3 + 4 = 7 \] So, the expression becomes: \[ 7 - 3\sqrt{5} \]
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Since there is no imaginary part, we can express the result in standard form \( a + bi \) where \( a = 7 - 3\sqrt{5} \) and \( b = 0 \).
Thus, the expression \( 3 + 4 - \sqrt{45} \) as a complex number in standard form is: \[ (7 - 3\sqrt{5}) + 0i \] or simply \( 7 - 3\sqrt{5} \).
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